Khba has (n) friends, each standing on a line at position (a_i), and each of them is in the range (0, x). They all want to come to him. One of his friends, Isamatdin, gave him (k) teleports. Each friend will walk to the nearest teleport (choosing the shortest distance). Once a friend reaches a teleport, khba and the friend can instantly meet. But khba is so tired that he'll be sleeping while his friends are walking toward him. Now he wants to choose (k) teleport positions so that their positions are distinct and lie within the range (0, x), in order to maximize the time it takes for the first friend who reaches a teleport to reach it. Assume that friends move at the same speed. Since khba isn't good at calculations, you should output the (k) chosen teleport positions. Each test contains multiple test cases. The first line contains a single integer (t) ((1 \leq t \leq 10^4)) — the number of test cases. The description of the test cases follows. The first line of each test case contains three integers (n), (k), and (x) ((1 \leq n, k \leq 2 \cdot 10^5), (k - 1 \leq x \leq 10^9)) — the number of friends, the number of teleports, and the range of possible positions for the teleports. The second line of each test case contains (n) integers (a_1, a_2, \dots, a_n) ((0 \leq a_i \leq x)) — the positions of khba's friends. It is guaranteed that the sum of (n) over all test cases does not exceed (2 \cdot 10^5). It is guaranteed that the sum of (k) over all test cases does not exceed (2 \cdot 10^5). For each test case, output a single line containing (k) integers — the (k) chosen teleport positions. The positions must be distinct and lie within the range (0, x). The positions may be output in any order. If there are multiple optimal choices, output any of them. Sample 1. Friends at positions (1,0,2,4). Chosen teleport position: (3). Nearest teleport for eac